1. Field of the Invention
This invention pertains to the field of electromagnetic devices in the form of resonators and frequency filters.
2. Description of Related Art
A resonator is typically defined as a device that exhibits resonance at a particular frequency, such as an acoustic resonator or cavity resonator. Electronic devices in the form of resonators are often geometrical arrangements of conductors, dielectrics, magnetic materials, etc., where an electromagnetic wave can exist at only discrete resonant frequencies. These resonant frequencies are those frequencies at which Maxwell""s equations and the boundary conditions and or field matching conditions imposed by the geometry of the structure can simultaneously be satisfied. Examples of resonators using boundary conditions to establish resonant frequencies are transmission lines, such as micro strip and rectangular waveguides, where boundary conditions are placed a half-wavelength apart for the lowest resonant frequency along the transmission line. Alternatively, field matching conditions can be used to establish a resonant condition using the transmission line, the microstrip ring resonator being a prime example. The requirement that the electromagnetic fields be continuous imposes a resonant condition by requiring that the circumference of the ring be an integer number of wavelengths. The symmetry of a ring resonator results in two orthogonal degenerate modes of sin xcex8 and cos xcex8 angular dependency. Resonators with degenerate modes are often not the best choice for a simple resonator since any lack of perfect symmetry leads to a splitting of the degeneracy and the result is two resonances with nearly the same frequency. However, this same property can be quite useful when implementing filters, since n dual-mode resonators can be used to implement a 2n-pole filter, whereas it would require 2n single-mode resonators to realize a 2n-pole filter.
Although there are many different resonator geometries including rectangular waveguides, microstrips, and dielectrically loaded cavities, the physical size of any particular resonator type is largely determined by the wavelength of the electromagnetic wave at the resonant frequency. Common to these resonators is the fact that an electromagnetic wave must experience a change in phase along the geometry of the structure. The phase change required over the geometry is dependent on the boundary and or field matching conditions that must be satisfied, but is most often one quarter, one half, or one wavelength long. Given a particular uniform structure, the size is largely determined by the phase change that must be experienced in order to satisfy the boundary and or field matching requirements.
The Mobius strip is a known concept. It is perhaps the most well known surface that falls within the study of topology. The Mobius strip has several interesting properties for a finite three dimensional object: it has only one surface and only one edge. The deformation of the rectangle that takes place in forming a Mobius strip is a rotation of the geometry through 180 degrees. At a particular frequency, f, if a section of transmission line a half wavelength long were bent back on itself, resonance could not occur as the field would not match. Indeed, the wave at both xe2x80x9cendsxe2x80x9d would be 180 degrees out of phase. The line would need to be a full wavelength long for this approach to yield a resonant condition, alternatively, it would have a resonant condition at a frequency of 2f.
It is an object of this invention to reduce size and/or weight of a resonator.
Another object of the invention is to reduce length of a wave, i.e., wavelength, and still obtain a resonant frequency.
Another object of the invention is to introduce at least one twist or cross-over, via a homoamorphic deformation, into a waveguiding structure and still come up with a resonant frequency.
These and other objects of this invention are attained by twisting a waveguiding structure so that a wave traveling on the waveguiding structure, where the ends of the strip resonator are found, is continuous and produces resonant frequency, the resonator having reduced size and/or weight.